I think the top-level US officials have said little. OTOH they did dispatch Samantha Power--the Administrator of USAID--to the region, who has been more vocal:
U.S. envoy Samantha Power accused Azerbaijan of having orchestrated a nine-month blockade of Nagorno-Karabakh that “created excruciating humanitarian conditions,” adding that “the attacks of last week have made a dire situation even worse.”
The USAID administrator also called for international access to the region amid “very troubling reports of violence against civilians.”
(That statement appears to have been made on Tue, Sep 26.)
Interestingly, looking at her bio she seems to have written about genocide [prevention] in the past, to quite some extent. Also,
Asked by POLITICO whether she agreed with warnings from Armenia’s Prime Minister Nikol Pashinyan that the exodus reflected “ethnic cleansing,” Power — a former genocide scholar — declined to use the term.
However, she added, “testimony” was already being gathered “from people who have fled violence, deprivation, and with the fear of living under the government of Azerbaijan.”
“We have heard very troubling reports of violence against civilians,” she went on.
FWTW, there appears to be little or no Western press in the region now (as well). Except Al-Jazeera, apparently, which posted a long walk (in fact two) on an abandoned street in "Khankendi, formerly known as Stepanakert" as the presenter put it.
Ah, thanks to VOA (since no "mainstream" commercial press seems to have bothered to report this)
The U.S. State Department said Secretary of State Antony Blinken urged Azerbaijan President Ilham Aliyev in a phone call to assure people in Nagorno-Karabakh their rights will be protected and to allow for humanitarian access to the region.
“The secretary urged President Aliyev to commit to broad amnesty and allow an international observer mission into Nagorno-Karabakh, and noted the President’s public commitments to help build a future for all those in Nagorno-Karabakh based on peace, mutual understanding, and mutual respect,” State Department spokesperson Matthew Miller said in a statement.
As for "US had strict stands against Turkey on the issue". I don't quite recall. When was that? Is the "issue" Nagorno-Karabakh or are you referring to something else? Certainly the Trump administration seems to have cared just as little if not less, not taking part in the Minsk discussions at all. (Yeah, Trump did stand up to Turkey on other matters.) What Pompeo [back then] said was:
“Our view is that this has been a longstanding conflict between these two countries in this particular piece of real estate,” Pompeo told Fox News. “We’re discouraging internationalization of this. We think outsiders ought to stay out. We’re urging a ceasefire. We want them both to back up. We’ve spoken to the leadership in each of the two countries, asking them to do just that.”